Time evolution of a Vlasov–Poisson plasma with different species and infinite mass in R3

We study existence and uniqueness of the solution to the Vlasov–Poisson system describing a plasma constituted by different species evolving in R3, whose particles interact via the Coulomb potential. The species can have both positive or negative charge. It is assumed that initially the particles are distributed according to a spatial density with a power-law decay in space, allowing for unbounded mass, and an exponential decay in velocities given by a Maxwell–Boltzmann law, extending a result contained in Caprino et al. (J Stat Phys 169:1066–1097,2017), which was restricted to finite total mass.